You should clean out any new plate, bowl, cup, etc.
Pumping water through bottles, tubes, and filters will clean them to some extent- but physical contact is the most effective way to clean just about anything. Especially bottles- you can use bleach until you're (literally) red in the face, but the inside of a well-used Platy will still have a slimy texture until you actually clean the thing...
Bleach is generally overkill, especially in the way that it is used by many germaphobes. If that's your bag, use a low concentration and allow the tube and bottle to air dry. You don't have to wait for it to be entirely dry, but wait at least 10 minutes. Then rise well.
CDC recommends a concentration of 1 teaspoon per gallon of water for sanitizing food containers. You could safely use up to a 4 tablespoons, but I wouldn't use more than that- it's not going to do a better job of sanitation, and you'll still need to give it time to dry, etc. And rise it a lot more.